Runes

Unknown Section mastery

Introduction

Ever wondered if you should be buying health, or continue buying resistance? Then this guide is for YOU!

This is a mathematical guide on how to optimize your defenses. It should be useful for people who play tanks mostly, but hopefully lots of people will find it helpful.

Check out my other guide!!: http://www.solomid.net/guides.php?g=4844

Some people have asked where my xin guide is.. I removed it since it was outdated, will release a new one sometime in the future.

The Formula

Incoming damage is reduces by a factor, according to the formula below:

100/(100+Armor)

Examples:

1. Having 50 armor will multiply incoming physical damage by 2/3 (Blocks 1/3 of the damage)

2. Having 100 armor will multiply incoming physical damage by 1/2 (Blocks 1/2 of the damage)

3. Having 200 armor will multiply incoming physical damage by 1/3 (Blocks 2/3 of the damage)

Health

Lets start of by calculating the gold value of Health

AVERAGE cost of 1 Health: 2.6 gold

or

1 Gold buys you: 0.385 Health

Resistances

AVERAGE cost of 1 Armor: 15.9 gold

or

1 Gold buys you 0.063 Armor

AVERAGE cost of 1 Magic Resist: 15.8 gold

or

1 Gold buys you 0.0633 MR

As you can see these values are very close,so we can just round off:

Average cost of 1 Resistance = 15.85 gold

1 Gold buys you 0.062 Resistances

Effective Hp

I will introduce a new terminology "Effective HP"

Armor can be viewed as a sort of "bonus hp shield".

Then

EFFECTIVE HP = Health X (100 + Armor)/100

Example:

1. Having 50 armor and 1000 Health means you have 1500 EH

2. Having 100 armor and 1000 Health means you have 2000 EH

3. Having 200 Armor and 1000 Health means you have 3000 EH

A simple way to think of it is that every 1 Armor increases you EH by 1%

Optimization 1. (vs single type damage)

Here now comes the slightly tricky part:

1hp gives you 1+(AR/100) Effective HP

Examples:

1. Purchasing 1hp when you have 100 armor gives you 2 EHP
2. Purchasing 1hp when you have 200 armor gives you 3 EHP

1Armor gives you 0.01hp Effective Health

Examples:

1. Purchasing 1 armor when you have 1000 health gives you 10EHP
2. Purchasing 1 armor when you have 2000 health gives you 20EHP

BUT armor and Health have different gold values!! Which is why we calculated it early so we substitute them:

1 Gold of Hp gives you (0.385 + 0.00385AR)EHP

and

1 Gold of Armor gives you (0.00062HP) EHP

We then equate these value to find a SWEET SPOT

(0.00062HP) = (0.385 + 0.00385AR)

HP = 6.2AR + 620

This equation tells us when HP and armor are of Equal Value

Basically you always want your health to equal 620+6.2AR. If your health is greater than this purchase armor, if lower purchase health.

A simple way to think of it is a graph in which we try to follow the plotted line as closely as possible:

If above the plotted line... purchase Armor

If below the plotted line purchase Health

Sweet Spot Values

At 620 hp....0 Armor

At 1000 hp...61 Armor

At 1500 hp...141 Armor

At 2000 hp...222 Armor

At 2500 hp...303 Armor

At 3000 hp...383 Armor

Optimization 2. (vs split damage)

The above is calculations are all good when facing a team that does only Physical damage. Now lets consider a team that does split Physical AND magical damage, then health becomes better valued since it blocks both types of damage, where as purchasing armor only blocks one type.

A simple way to think of it is a graph in which we try to follow the plotted line as closely as possible:

If above the plotted line... purchase Resistances

If below the plotted line purchase Health

Sweet Spot Values

At 1241 hp....0 Armor and MR

At 1500 hp...21 Armor and MR

At 2000 hp...61 Armor and MR

At 2500 hp...101 Armor and MR

At 3000 hp... 141.7 Armor and MR

At 3500 hp...182 Armor and MR

At 4000 hp...222 Armor and MR

TLDR

Ideally we would like to follow the line increasing our hp and armor bit by bit following the "Sweet spot" line. Sadly this is not possible in game, so I have made a list of "checkpoints" for people to follow.

Important: Due to enemy penetration, it is always better to overshoot on the resistance side rather then health.

Against single type damage

Aim for 60 Armor/MR then get 1000 Health

Then 150 Armor/MR then get 1500 Health

Then 220 Armor/MR then get 2000 Health

Then 300 Armor/MR then get 2500 Health

Then 380 Armor/MR then get 3000 Health

Against a balanced team (Physical and Magical)

Get 1500 Health

Aim for 60 Armor and Magic Resist then 2000 Health

Then 100 Armor and Magic Resist then 2500 Health

Then 150 Armor and Magic Resist then 3000 Health

Finish of with 200 Armor and Magic Resist.

Factors to Consider

This theory crafting is all good, but the game is very complex and we have to take some factors into consideration. That being said... THIS GUIDE SHOULD BE TAKEN AS A GENERAL GUIDELINE, AND YOU SHOULD USE YOUR OWN COMMON SENSE WHEN MAKING JUDGEMENT CALLS.

FACTORS TO CONSIDER

1.Enemy Penetration should be taken into account. Most AD carries have roughly 30 Armor pen. Most AP carries have roughly 15 Magic pen, or 40 with

Now lets analyze and make assumptions on what happens when he gets into a early team fight at dragon.

He Q's someone for 10%(assume they have mr) of their health (roughly 1000) so his Q does 100 damage and heals him for 80.

He then autoattacks 3 times to gain 76 health.

He takes alot of damage and decides to ultimate someone hitting them 5 times. During this time he is considered to have full stacks of his passive, and 30% lifesteal... so he will gain roughly 180 + 80 health for a total of 260 health

Immediately after his ult he Q's them again and heals for 80 again, before dieing.

So far he has gained a total of 496 Health.

With this in-mind we can then assume that he effectively has roughly 1500 Health and 60 Armor and 60 MR... with no items. Pretty good

Our next goal will be 2000 hp, so we grab a

LEVEL 11

Level 11 with

Will have 1850 Health
With 118 Armor and 123 Mr

Another team fight at dragon...
He Q's for 20% of max health (2000) 400 damage which is reduced by mr to 200. He heals for 80% of this 160.

He then autoattacks 3 times again healing for 108

He Q's a second time healing 160 again

Then he ults Healing for 270 + 120 = 390 Health

He Q's again 160

So effectively he has roughly 1000 bonus health from QX3, 3 autoattacks, and his ultimate.

So now we are sitting at 2850 Health and 118 Armor and 123 Mr

Our next goal will be 200 Armor and Mr

Level 18

Will have 2580 Health
and 265 Armor and 270 MR

A teamfight at Baron this time: in which he will heal for 1000+ (see above calculations)

@McWut You are wrong. Leagucraft calculates the average of E(physicaldmg)HP and E(magicaldmg)HP; this isnt the EHP against split damage; Also isnt this guide about getting the highest possible EHP but about getting high EHP in relation to cost-efficiency.

On leaguecraft.com/builder, I tried to get the maximum possible EHP on rammus.

The optimal build I found was Warmog's x3 and Guardian Angel x2 + Mercury's treads. This gives him 6,000 health, 244 armor and 150 magic resist for 15,400 gold. That's 17,800 EHP against balanced damage. That is the highest EHP I could build and I tried a lot of different things. So it seems that your guide is a little off.